Equation 677 Database

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Magma ece80fd0604a…

magma ece80fd0604a
Size
705
Isomorphism class hash
ece80fd0604abeadc0f0a654ce361cf6514097c7f4b0f41eaa15a81dd4018ab2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 15:51:45
Display reorder
660,406,405,407,404,402,403,396,397,398,399,400,401,446,444,445,449,447,448,452,450,451,455,453,454,299,297,298,295,296,294,290,288,289,293,291,292,152,150,151,155,153,154,147,148,149,146,144,145,333,334,335,332,330,331,324,325,326,327,328,329,671,680,682,686,119,118,117,114,115,116,109,110,108,112,113,111,601,602,600,604,605,603,607,608,606,610,611,609,124,125,123,120,121,122,130,131,129,126,127,128,547,548,546,550,551,549,545,543,544,541,542,540,481,482,480,484,485,483,487,488,486,490,491,489,661,664,666,670,625,624,626,627,628,629,630,631,632,633,634,635,507,508,509,506,504,505,513,514,515,512,510,511,212,210,211,215,213,214,207,208,209,206,204,205,570,571,572,573,574,575,568,569,567,564,565,566,237,238,239,236,234,235,228,229,230,231,232,233,674,678,677,685,319,318,320,321,322,323,316,317,315,312,313,314,74,72,73,77,75,76,80,78,79,83,81,82,432,433,434,435,436,437,438,439,440,441,442,443,394,395,393,390,391,392,385,386,384,388,389,387,67,68,66,70,71,69,65,63,64,61,62,60,697,699,700,704,163,162,164,165,166,167,160,161,159,156,157,158,5,3,4,0,2,1,11,9,10,7,8,6,636,637,638,639,640,641,642,643,644,645,646,647,521,519,520,517,518,516,527,525,526,523,524,522,583,584,582,586,587,585,581,579,580,577,578,576,689,693,694,695,280,279,281,278,276,277,285,286,287,284,282,283,248,246,247,251,249,250,243,244,245,242,240,241,258,259,260,261,262,263,256,257,255,252,253,254,270,271,272,273,274,275,268,269,267,264,265,266,174,175,176,177,178,179,172,173,171,168,169,170,663,669,667,676,614,613,612,616,617,615,619,620,618,622,623,621,19,20,18,22,23,21,17,15,16,13,14,12,501,502,503,500,498,499,492,493,494,495,496,497,226,227,225,222,223,224,217,218,216,220,221,219,557,555,556,553,554,552,563,561,562,559,560,558,688,691,692,696,650,649,648,652,653,651,655,656,654,658,659,657,531,532,533,530,528,529,537,538,539,536,534,535,135,136,137,134,132,133,141,142,143,140,138,139,598,599,597,594,595,596,589,590,588,592,593,591,469,470,468,472,473,471,475,476,474,478,479,477,675,690,683,684,197,196,195,192,193,194,202,203,201,198,199,200,48,49,50,51,52,53,54,55,56,57,58,59,351,352,353,350,348,349,357,358,359,356,354,355,36,37,38,39,40,41,42,43,44,45,46,47,415,416,414,418,419,417,413,411,412,409,410,408,698,701,702,703,101,100,99,96,97,98,106,107,105,102,103,104,366,367,368,369,370,371,364,365,363,360,361,362,379,380,378,382,383,381,377,375,376,373,374,372,90,91,92,93,94,95,88,89,87,84,85,86,428,426,427,431,429,430,423,424,425,422,420,421,662,665,668,673,460,459,461,458,456,457,465,466,467,464,462,463,311,309,310,307,308,306,302,300,301,305,303,304,186,187,188,189,190,191,184,185,183,180,181,182,344,342,343,347,345,346,339,340,341,338,336,337,32,30,31,35,33,34,27,28,29,26,24,25,672,679,681,687 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, M = {62} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 15:51:48 · history